What is the name of the mathematical theorem stating that for any continuous function on a closed interval, there must be a point where the function reaches any value between its endpoints?

The question describes the Intermediate Value Theorem. This theorem states that if a function $f$ is continuous on a closed interval $[a, b]$, and $k$ is any number between $f(a)$ and $f(b)$, then there must exist at least one number $c$ in the interval $[a, b]$ such that $f(c) = k$.

The correct answer is A.

$$\boxed{\text{A. Intermediate Value Theorem}}$$